scholarly journals Antiperiodic Solutions to Impulsive Cohen-Grossberg Neural Networks with Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanqin Wang ◽  
Maoan Han
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Scales ◽  
Time Scale ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Coincidence Degree

We use the method of coincidence degree and construct suitable Lyapunov functional to investigate the existence and global exponential stability of antiperiodic solutions of impulsive Cohen-Grossberg neural networks with delays on time scales. Our results are new even if the time scaleT=RorZ. An example is given to illustrate our feasible results.

Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen-Grossberge neural networks on time scales

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Jingzhong Liu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Existence And Stability

AbstractBy applying the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

scholarly journals Existence and Stability of Periodic Solutions for Impulsive Fuzzy Cohen-Grossberg Neural Networks on Time Scales

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Qianhong Zhang ◽  
Jingzhong Liu ◽  
Yuanfu Shao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Globally Exponential Stability ◽  
Existence And Stability

Abstract By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

GLOBAL EXPONENTIAL STABILITY OF FUZZY INTERVAL DELAYED NEURAL NETWORKS WITH IMPULSES ON TIME SCALES

2009 ◽  
Vol 19 (06) ◽  
pp. 449-456 ◽  
Author(s):  
YONGKUN LI ◽  
TIANWEI ZHANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Delayed Neural Networks ◽  
The Neural Networks ◽  
Uniqueness Of Equilibrium ◽  
Fuzzy Interval

In this paper, we investigate the existence and uniqueness of equilibrium point for fuzzy interval delayed neural networks with impulses on time scales. And we give the criteria of the global exponential stability of the unique equilibrium point for the neural networks under consideration using Lyapunov method. Finally, we present an example to illustrate that our results are effective.

scholarly journals The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 321 ◽  
Author(s):  
Bing Li ◽  
Yongkun Li ◽  
Xiaofang Meng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays

In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.

scholarly journals Existence and Global Exponential Stability of Equilibrium Solution to Reaction-Diffusion Recurrent Neural Networks on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Kaihong Zhao ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Exponential Stability ◽  
Time Scales ◽  
Recurrent Neural Networks ◽  
Global Exponential Stability ◽  
Equilibrium Solution ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. One example is given to illustrate the effectiveness of our results.

scholarly journals Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yaping Ren ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Time Scale ◽  
Cellular Neural Networks ◽  
Activation Functions ◽  
State Dependent ◽  
Existence Of Periodic Solutions

We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale𝕋=ℝorℤand improve some of the previously known results.

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